As is well known and understood, the frequency-temperature characteristic of quartz crystal resonators depends primarily on the angle of cut of the quartz plate with respect to the natural crystallographic axes. Precision crystal oscillators often require accurate control of the crystal blank's angle of cut to satisfy imposed stability requirements. Where X-ray diffraction techniques are employed as a means of measuring the angle of cut, an accuracy in the order of a few seconds is desirable in order to attain a high manufacturing yield.
As is also known, particular difficulty is encountered in the case of circular crystal plates, where measurement uncertainties of up to one to two minutes of arc have commonly been experienced. Whereas complex X-ray goniometer systems have been suggested to produce an increased accuracy in measurement precision, it has been found that errors continue to persist; and that this, in part, results from the fact that the goniometer generally measures the angle between the atomic plane of the crystal and a reference plane in the goniometer to which the crystal plate is secured, whereas it is the angle between the atomic plane and the plate face which is sought to be measured. Analysis has shown that the atomic plane and the goniometer reference plane may not necessarily be parallel -- but, in fact, may be angled, because of imprecise vacuum chuck arrangement, because of dust particles present in the system mounting points, and because pressures may vary inside the vacuum chuck. Additionally, the uncertainty in defining the peak of the X-ray rocking curve, imprecision in the 90.degree. rotations about the plate face normal, and tilt in the plate so that the plate face was not perpendicular to the plane of the goniometer, were other sources of inaccuracy. Some of these sources of error were determined to be inherent, and seemingly unavoidable, in the mechanical operation of the X-ray goniometer.